A NAND type flash memory is known as a nonvolatile semiconductor memory device that is electrically rewritable and capable of a high degree of integration. Moreover, a memory system configured having a plurality of NAND type flash memory chips (hereinafter, referred to simply as “memory chip”) controlled by one controller is also becoming widely used. In such a memory system comprising a plurality of memory chips, it is becoming common that in order to improve system performance, the plurality of memory chips are operated in parallel. In that case, it may occur that a peak current of the plurality of memory chips is concentrated in a certain time period. There is a risk that such a concentration of the peak current causes a drop in a power supply voltage, thereby causing such problems as a system malfunction, and so on.